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Equivalence between the internal observability and equation

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 89-97页

作者： LIU Wen-jun TU Zhi-yu School of Mathematics and statistics Nanjing University of Information Science and TechnologyNanjing 210044China

This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave *** by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.

关键词： Moore-Gibson-Thompson equation internal observability exponential stability

The stable Auslander-Reiten components of certain monomorphism categories

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Science China Mathematics 2024年第3期67卷 505-526页

作者： Rasool Hafezi Yi Zhang School of Mathematics and statistics Nanjing University of Information Science and TechnologyNanjing 210044China

Let Λ be an Artin algebra and let Gprj-Λ denote the class of all the finitely generated Gorenstein projective Λ-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a certain subcategory of the monomorphism category S(Gprj-Λ) containing boundary vertices. We describe the shape of such components. It is shown that certain components are linked to the orbits of an auto-equivalence on the stable category Gprj. In particular, for the finite components, we show that under certain mild conditions,their cardinalities are divisible by 3. We see that this three-periodicity phenomenon reoccurs several times in the paper.

关键词： monomorphism category almost split sequence Auslander-Reiten quiver Gorenstein projective module

On Leray's problem in an infinitely long pipe with the Navier-slip boundary condition

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Science China Mathematics 2024年第4期67卷 819-854页

作者： Zijin Li Xinghong Pan Jiaqi Yang School of Mathematics and statistics Nanjing University of Information Science and TechnologyNanjing 210044China School of Mathematics and Key Laboratory of Ministry of Industry and information technology Nanjing University of Aeronautics and AstronauticsNanjing 211106China School of Mathematics and statistics Northwestern Polytechnical UniversityXi'an 710129China

The original Leray’s problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe,which approach the Poiseuille flow subject to the no-slip boundary condition at spatial *** this paper,the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition,is *** to the complexity of the boundary condition,some new ideas,presented as follows,are introduced to handle the extra difficulties caused by boundary ***,the Poiseuille flow in the semi-infinite straight pipe with the Navier-slip boundary condition will be introduced,which will serve as the asymptotic profile of the solution to the generalized Leray’s problem at spatial ***,a solenoidal vector function defined in the whole pipe,satisfying the Navierslip boundary condition,having the designated flux and equalling the Poiseuille flow at a large distance,will be carefully *** plays an important role in reformulating our ***,the energy estimates depend on a combined L2-estimate of the gradient and the stress tensor of the velocity.

关键词： stationary Navier-Stokes system Navier-slip boundary condition Leray's problem

Aubry-Mather theory for contact Hamiltonian systems Ⅲ

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Science China Mathematics 2024年第11期67卷 2541-2570页

作者： Panrui Ni Lin Wang Shanghai center for Mathematical Sciences Fudan University School of Mathematics and statistics Beijing Institute of Technology

By exploiting the contact Hamiltonian dynamics（T*M × R,Φ_t） around the Aubry set of contact Hamiltonian systems,we provide a relation among the Mather set,the Φ_t-recurrent set,the strongly static set,the Aubry set,the Ma?é set,and the Φ_t-non-wandering ***,we consider the strongly static set,as a new flow-invariant set between the Mather set and the Aubry set in the strictly increasing *** show that this set plays an essential role in the representation of certain minimal forward weak Kolmogorov-Arnold-Moser（KAM） solutions and the existence of transitive orbits around the Aubry set.

关键词： Aubry-Mather theory weak KAM theory contact Hamiltonian systems Hamilton-Jacobi equations

An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions

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Chinese Physics B 2024年第7期33卷 117-124页

作者：魏姣耿献国王鑫 School of Mathematics and statistics Zhengzhou UniversityZhengzhou 450001China School of Mathematics and information Science Zhongyuan University of TechnologyZhengzhou 450007China

Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

关键词： Darboux transformation soliton solutions generalized Fokas–Lenells equation

Fault-tolerant identity-based encryption from SM9

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Science China(information Sciences) 2024年第2期67卷 104-117页

作者： Xiaohong LIU Xinyi HUANG Zhaohui CHENG Wei WU Fujian Provincial Key Laboratory of Network Security and Cryptology College of Computer and Cyber SecurityFujian Normal University Artificial Intelligence Thrust Information HubThe Hong Kong University of Science and Technology (Guangzhou) Olym information Security technology Ltd. center for Applied Mathematics of Fujian Province School of Mathematics and StatisticsFujian Normal University

This paper initiates the formal study of attribute-based encryption within the framework of SM9,the Chinese National Cryptography Standard for Identity-Based Cryptography, by presenting two new faulttolerant identity-based encryption(FIBE) schemes. Our first scheme uses the same private-key/ciphertext structure as the original SM9 algorithm and operates in a small attribute universe. As a result, it can be effectively and smoothly integrated into the information systems using SM9. In the random oracle model,we prove that our scheme is ciphertext-indistinguishable against fuzzy selective-identity and chosen-plaintext attacks under the(k + 3)-DBDHI assumption. Our second design is a large universe FIBE scheme based on SM9 that is ciphertext-indistinguishable against chosen-plaintext attacks in the random oracle model under the(f, g)-GDDHE assumption. Finally, we compare the communication and computing costs of our schemes to those of other classical ones. The comparison shows that our schemes have comparable performance as others. We believe that our findings will accelerate the applications of SM9 in modern information systems such as cloud computing and blockchain.

关键词： attribute-based encryption identity-based encryption fault-tolerant SM9

Joint modulation format identification and OSNR monitoring based on Stokes vector distribution features for digital coherent optical receivers

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Chinese Optics Letters 2024年第5期22卷 22-28页

作者：蒲正宇蒋林闫连山易安林何海军潘炜罗斌 center for information Photonics&Communications School of Information Science and TechnologySouthwest Jiaotong UniversityChengdu 611756China

For joint modulation format identification(MFI)and optical signal-to-noise ratio(OSNR)monitoring,a simple and intelligent optical communication performance monitoring method is proposed,and the feasibility is demonstrated by digital coherent optical communication *** experiment results show that for all modulation formats,including 28 GBaud polarization division multiplexing(PDM)QPSK/8-QAM/16-QAM/64-QAM,100%MFI accuracies are achieved even at OSNR values lower than the corresponding theoretical 20%forward error correction limit,as well as the high accuracies for OSNR ***,the proposed scheme has a reasonable monitoring level when chromatic dispersion and fiber nonlinear effects are varied.

关键词： coherent communication optical performance monitoring deep neural network

Quantum key distribution over a mimicked dynamic-scattering channel

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Science China(information Sciences) 2024年第4期67卷 323-330页

作者： Qi-Hang LU Fang-Xiang WANG Wei CHEN Hai-Yang FU Yin-Jie LU Shuang WANG De-Yong HE Zhen-Qiang YIN Guang-Can GUO Zheng-Fu HAN CAS Key Laboratory of Quantum information University of Science and Technology of China CAS center for Excellence in Quantum information and Quantum Physics University of Science and Technology of China Hefei National Laboratory University of Science and Technology of China

Free-space quantum key distribution(QKD) plays an important role in the global quantum network. However, free space channels suffer from the atmospheric turbulence and scattering effects of haze,fog, and dust, which significantly weaken the performance of QKD or even block the secure quantum ***, we prove the performance of QKD over a dynamic scattering channel can be enhanced significantly using a fast wavefront shaping technique. The system achieves on average 10-dB enhancement of quantum transmission efficiency and establishes a secure quantum link for QKD. Our work demonstrates the feasibility of QKD through free-space dynamic scattering channels and enhances the deployment capability of complex-channel QKD system.

关键词： quantum key distribution free space channel channel turbulence channel scattering wavefront shaping

THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT

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Acta Mathematica Scientia 2024年第2期44卷 671-685页

作者：夏晓宇闫理坦杨晴 College of information Science and technology Donghua UniversityShanghai201620China Department of statistics College of ScienceDonghua UniversityShanghai201620China

Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<*** this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)dt+vdt-θ(∫_(0)^(t)(X_(t)^(H)-X_(s)^(H))ds)dt,whereθ<0,σ,v∈ℝ.The process is an analogue of self-attracting diffusion(Cranston,Le *** Ann,1995,303:87–93).Our main aim is to study the large time behaviors of the *** show that the solution X^(H)diverges to infinity as t tends to infinity,and obtain the speed at which the process X^(H)diverges to infinity.

关键词： fractional Brownian motion stochastic difference equations rate of convergence asymptotic